Estimating and interpreting hydrological drought indices using a
selected catchment in Zimbabwe
Washington R Nyabeze*
Water Systems Research Group, University of the Witwatersrand, Postnet Suite 385, Private Bag X1, Jukskei
Park, 2153, Johannesburg, South Africa.
Abstract
A distributed modeling approach is applied at a scale that permits visualization of
hydrological drought conditions in different tertiary catchments. Hydrological drought
sequences are calculated from runoff time-series data. Statistics of runoff and drought impact
information from literature are applied to classify hydrological droughts on magnitude,
duration, recurrent interval and impact to define a set of hydrological drought indices for
specific conditions. The indices are applied on a sample of hydrological drought seasons in a
selected primary catchment and visualized in a geographical information software. Scenarios
are created to identify worst cases.
Keywords: Distributed Modeling, Partial Duration Series, Drought Sequences, Drought
Visualization, Hydrological Drought Impacts, Hydrological Drought Indices
*
Corresponding author
Email address: icu@dwaf.gov.za or wedswrn@icon.co.za
1. Introduction
The Mzingwane catchment forms parts of Matabeleland North, Matabeleland South, the
Midlands and Masvingo provinces, which were amongst the most affected by recent droughts.
The provincial coverage is shown in Figure 1.This catchment is the main source of water for
Bulawayo, Zimbabwe’s second largest city. The yield from the developed surface water
resource falls short of the demand, deficits being more evident during droughts. This
interesting situation inspired the author to select the Mzingwane primary catchment for
investigative research.
Figure 1.
2. Hydrological droughts
This research adopted the definition of hydrological droughts introduced by Yevjevich (1967)
where a threshold, q 0 is defined below which the flow of a stream becomes a drought flow.
This approach allows simultaneous characterization of stream flow droughts in terms of
stream flow, q , duration and frequency of occurrence. Thus runoff at a point is expressed in
millimetres and the period is defined by the duration.
3. Threshold selection
2
A specific requirement can be used to define the cut-off or threshold for a drought. Dracup et
al (1980) suggests that a threshold be a function of the type of water deficit being studied. For
example in analysing impact on yield of reservoirs a threshold may be a specific yield from a
reservoir. It is also possible to apply a percentage of mean flow or a percentage from the flow
duration curve.
A threshold is regarded as fixed if a constant value is used for the whole series. A threshold
derived from the flow duration curve of annual runoff, for example a flow exceeded 90% of
the period of analysis can be referred to as q 90 . The monthly varying threshold defined in
Demuth et al. (2000) could not be applied on this research because with the high variability of
flow across months low flow in a month can be compensated by high flow in another
effectively cancelling out potential deficits on the annual scale.
Figure 2
The SPA was also applied in drought studies in Rosbjerg (1987) and Rosbjerg et al (1992).
Figure 2 illustrates the application of mean annual runoff ( q ave ) as a fixed threshold. The
annual runoff at the outlet to secondary catchment NC in Mzingwane was 79.6mm. With
q ave droughts lasting one year are frequent and a drought spanning six years was experienced
during the period 1981/82 to 1987/88. Four-year hydrological droughts were also experienced
from 1967/68 to 1971/72 and from 1988/89 to 1992/93. The median annual flow ( q 50 ) for the
outlet to NC was 62.6mm, which was lower than the mean thus if the threshold is adjusted to
q 50 then some of the minor droughts would no longer be classified as hydrological droughts.
This example shows that the application of runoff estimated on this research makes it possible
3
to investigate droughts at different thresholds and determine droughts of multi-year durations,
which would not be possible with the short span of observed data.
4. Sequential analysis
In analysing hydrological droughts dependency among droughts and the presence of minor
droughts can be avoided by pooling to define an independent sequence of droughts. A partial
duration series is then set up consisting of all events that do not exceed a specified threshold.
Kjedsen et al. (2000) showed that the sequential peak algorithm (SPA) traditionally used for
flood analysis can be applied in reverse to pick up low flows in a procedure, which generates
a partial duration series of drought flows. According to Tallaksen et al. (1997) the moving
average (MA) pooling procedure can smooth a time series using the moving average as a
filter. The MA requires prior knowledge of the averaging interval and average of the timeseries. The main advantage of the MA polling method is that it reduces the problem of minor
droughts and at the same time as mutually dependent droughts are pooled. The SPA method
on the other hand has a more straightforward interpretation as the results can be used directly
(Kjedsen et al., 2000). The SPA method was applied on this research and the threshold
q ave was defined as the mean of a partial duration series.
The Hydrological Drought Analysis Model developed on this research was programmed to
derive drought flows for durations of 1,2,3,4 and 5 years and present the results as tables and
graphs. A table shows values as calculated while a graph allows interpolation of runoff at
more commonly used recurrence intervals. The curves can be smoothed by interpolation. The
length of data determined the upper limit of recurrence interval.
To demonstrate the
application of the table and graph the 1:50 year and 1:10 year flows for the different durations
4
determined from a runoff data stretching 54years for secondary catchment NC are shown in
Figure 3.
Figure 3
A drought lasting one year occurs once every 3 years and on average drought flow of about
42.1mm would be experienced at the outlet to NC as shown in Figure 13. Estimates of the
1:50 drought flows of duration 1, 2, 3, 4 and 5 year were 12.6mm, 30.5mm, 53.2mm,
115.8mm and 147.2mm respectively. For the 1:10 year drought runoff was extrapolated from
the 1:11 year drought flow for the five-year duration and the 1, 2, 3 and 4-year drought flows
were 19.9mm, 81.6mm, 157.5mm and 248.9mm respectively.
5. Analyzing regional droughts
Severity of a drought is related to the extent of the area affected by it. Santos (1983)
suggested distinguishing between local and regional droughts by assessing the area affected.
On this research the regional aspect was explored by generating annual runoff statistics using
tertiary catchments. The threshold level method was then applied to each of them. The
percentage of the total primary catchment in a drought was determined. In this way severity
and frequency was related to the area affected.
6. Exposure to risk of hydrological droughts
5
To investigate tertiary catchments with the same risk of exposure to drought flows within a
given duration drought flow statistics for all tertiary catchments in Mzingwane were
generated. Runoff was then divided into categories for visualisation. The tertiary catchments
and the total area falling in the three lowest categories for 1: 50 and 1:10 years recurrence
intervals and durations of 1 to 5 years were assessed. Figure 3 illustrates results for a drought
of 1year duration.
Figure 4
About 24% of the primary catchment has inadequate data for analysis at the 1: 50:1 year
drought as shown in Figure 4. The minimum flow was 0.72mm and 58% of the area fell into
the category [0< 10mm] comprising mainly of the middle and lower cascaded secondary
catchments, the whole of secondary catchment N1 and the upper part N2. About 8% of the
catchment was in the category [10<15mm] and 10% in the category [15<50mm]. Thus 76%
of the catchment can generate between 0.72mm and 50mm during a 1year drought occurring
once in 50years taken from the runoff data analysed. The situation with a 1: 10, 1year drought
taken from the same runoff data is also illustrated in Figure 4. Estimates showed a minimum
flow of 0.48mm and about 48% of the area fell into the category [0<10mm] comprising
mainly of the middle and lower cascaded secondary catchments and the central part of
secondary catchment N2. About 20% of Mzingwane fell into the [10<15mm] category and
30% into the [15<50mm] category and the spread is shown in Figure 4. Thus considering the
1year drought that occurs 1: 10 years taken from the runoff data analysed, about 98% of
Mzingwane catchment can generate between 0.48mm and 50mm
6
7. Other options to view and analyze hydrological droughts
In the USA drought intensity categories are based on six key indicators and numerous
supplementary indicators (http://www.drought.unl.edu/). The drought severity indices include
the Palmer Drought Index, a Soil Moisture Model (Percentiles), Weekly Streamflow
(Percentiles), Standardized Precipitation Index and Satellite Vegetation Health Index.
Additional indices used include the Topsoil Moisture Index, Crop Moisture Index, a River
Basin Average Precipitation index and the Surface Water Supply Index. Maps are drawn
based on the key indices. The USGS WaterWatch applies a simple index to indicate current
conditions in rivers and streams relative to historical conditions (http://water.usgs.gov/cgibin/).
On this research, spatial views were developed to characterize estimated stream flow across a
primary catchment against drought or exceedance flows. More importantly indices were
calculated to translate the drought conditions into a form that is easier to interpret as follows:
(i)
An index, obtained by dividing annual runoff by the long-term mean annual
runoff. This allows comparison of the deviation from average conditions.
(ii)
An index, which compares annual runoff with flow at selected exceedences.
(iii)
An index obtained by dividing cumulative runoff for durations of 1 to 5 years by a
drought flow of the same duration but of any selected recurrence interval taken
from the length of data being analysed.
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(iv)
A water requirement index for durations of 1 to 5 years to a drought flow of the
same duration but of any selected recurrence interval taken from the length of data
being analysed.
An anomaly index was calculated by subtracting an index from 1 and was only relevant where
the index was less than 1, because in this situation by definition a hydrological drought would
exists. Calculation of anomaly indices is quite simple and is not discussed any further in this
paper.
8. Indexing runoff on mean annual runoff (MAR)
Estimates of drought flows during the period covering the seasons 1984/85 to 1993/94 were
indexed on MAR. The results are presented in Figures 5 to 9 discussed in this paper.
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 5 and Table 1 show that during the 1984/85 season 57% of Mzingwane experienced a
hydrological drought. This affected mainly the south-west part of the catchment. During the
following season the drought condition worsened for most of the affected tertiary catchments
and the drought coverage extended to 99% of Mzingwane. The drought runoff generated
8
deteriorated further during the1986/87 season the drought affected whole primary catchment
as shown in Figure 6. The same figure shows remarkable recovery for the 1987/88 season
with only 12% of the primary catchment still in drought. However the catchment was again in
a drought the following season as shown in Figure 7 and there was a slight improvement at
the regional level in 1989/90. However, less runoff was generated in parts of secondary
catchments S2 to S5 and T1 to T4. Further improvements were registered in 1990/91 for most
catchments but there was notable deterioration in secondary catchments B2, N2 and N3. The
1991/92 season was a hydrological drought and it affected the whole of Mzingwane as shown
in Figure 8 The comparisons in Table 1.2 indicate that 97% of Mzingwane generated less than
50% of the respective tertiary catchment MAR which was close to the 93% during the
1986/87 drought but the two droughts differed that the 1991/92 drought had nearly three times
more area generating less than 25% of its MAR. The drought condition improved in 1992/93
and 1993/94 but there was deterioration at the local level in 1993/94.
The analysis in this section indicates that the 1991/92 was the worst hydrological drought
during the period of analysis. Parts of secondary catchment UZ1 experienced hydrological
droughts of less than 25% of MAR during the entire 10year period, parts of B1 and N1 were
on 9 years out of 10. This suggests very severe drought conditions persisting for longer
durations than can be revealed from sequential analysis of time series. The analysis also
shows the existence of droughts that affect a few quaternary catchments and those that affect a
whole primary catchment. The three years preceding 1991/2 were drought years but thereafter
runoff improved but Mzingwane does not come out of the drought for the remainder of the
period suggesting that indexing on the MAR may result in planning periods, which are very
too long a parameter equal to a lower value runoff may be more appropriate.
9
9. Indexing runoff on exceedence runoff
The 50% and 80% exceedence runoff was applied to the runoff estimated for the 1991/92
season to generate indices shown in Figure 10 It is evident that about 99% of Mzingwane
generated less than the 50% exceedence tertiary catchment runoff during this season and 89%
generated less than the 80% exceedences tertiary catchment runoff.
Figure 10
The 95% and 98% exceedences runoff were also applied to the 1991/92 runoff to generate an
index and the results are shown in Figure 11. The results show that about 44% of the
catchment generated less than the 95% exceedence tertiary catchment runoff and the figure
was about 18% for the 98% exceedences tertiary catchment runoff estimated from the
available data. The analysis in this section shows that if high exceedence runoff is applied as a
threshold on the 1991/92 runoff then the spatial extent of drought in Mzingwane falls except
for parts of the secondary catchments UZ1, B1 to B3 and N1 to N3 which generated less than
the 98% exeedence runoff. This observation suggests that although the 1991/92 affected the
whole of Mzingwane some tertiary catchments were affected more than others.
Figure 11
10
10. Indexing 1991/92 drought on droughts lasting 4years
The analysis in section 8.7.1 suggests the 191/92 came at the end of drought lasting four years
and considering the improvements in runoff thereafter assigning a 4year duration to this
drought appears to be realistic. In this section the 1991/92 drought was analysed by
considering indices on 1: 10 and 1:15; 4year droughts. The results are presented in Figure 12.
Tertiary catchments without adequate data for the analysis were also indicated.
Figure 12
The 1991/92 affected the whole of Mzingwane. The 1:10 four-year drought achieves 100%
coverage of Mzingwane while the 1:15, 4 year drought achieved 91% coverage suggesting
that the 1991/92 drought in Mzingwane was somewhere between these two droughts.
11. Possible application of results
The first attempt to provide a national-scale runoff picture for Zimbabwe was done by Wenell
(Wenell 1965) around 1965 and about 20 years later Kabell produced new estimates (Kabel
1984). The hydrological drought analysis tool developed on this research permits more
frequently updating of runoff estimates to better represent catchment characteristics and take
account of any changes in climatic and geophysical processes. Furthermore the runoff timeseries can be applied in estimating run-of-river yield and yield from storage, which are critical
for planning for and managing hydrological droughts. However in the absence of a water
11
balance it is difficult to quantify the impact of a hydrological drought on water requirements
for various sectors. In this section an attempt is made to relate the 1991/92 hydrological
drought situation to demographic patterns.
Figure 13 shows the population totals for
enumerator areas in Mzingwane with secondary and tertiary catchments superimposed and the
runoff for the1991/92 season indexed on the 1:10 year drought lasting 4years. The most
affected secondary catchments B1 to B2 and N1 were not very populated. However,
populated area of N2 and N3 were in a severe situation with less than 25% of the 1 in 10 year,
4 years runoff. For the 59% of Mzingwane with an index of 0.25mm to 0.75mm the runoff
generated during this season would have been adequate for human requirements and other
uses if water storage structures were available and had been operated considering inflows
equal to the 1: 10year 4 years runoff.
Figure 13
References
Dracup J.A., Lee K.S., Paulson E.G., 1980, On Definitions of Droughts, Water Resources
Research, Vol 16, No 2, pp297-302
Demuth S., Lehner B., Stahl K., 2000, Assessment of Vulnerability of a River System to
Drought in: Drought and Drought Mitigation in Europe, pp 209-219, Academic
Publishers, Dordrecht, The Netherlands
Dracup J. A., Lee K. S., Paulson E. G. Jr., 1980, On the Definitions of Drought, Water
Resources Research, Vol 16, No 2,pp297-302
12
Kabel T.C., 1984, An Assessment of Surface Water Resources of Zimbabwe and Guidelines
for Development Planning, Government of Zimbabwe
Kjeldsen T. R., Lundorf A., 1997, Drought Management and Modelling- Zimbabwe Case,
MSc Thesis, Technical University of Denmark
Kjeldsen T. R., Lundorf A, Rosbjerg D, 2000Use of a two Component Exponential
Distribution in Partial Duration Modelling of Hydrological Droughts in Zimbabwean
Rivers. Hydrological Science Journal, Vol 45, No 2 pp 285-298
Rosbjerg D., 1987 Partial Duration Series with Log-Normal Distributed Peak Values. In V P
Singh (ed) Hydrological Frequency Modelling 117-129, D Reidel Publishing Company
Rosbjerg D., Madsen H., Rasmussen P. F., 1992. Prediction in Partial Duration Series with
Generalised Pareto Distributed Exceedences, Water Resources Research, Vol 28, No 11,
pp 3001-3010
Santos M. A., 1983, Regional Droughts: A stochastic Characterisation, Journal of Hydrology,
vol 66, pp183-211
Tallaksen L. M., Clausen B, Mdsen H, 1997, On Definition and Modelling of Streamflow
Drought Duration Deficit volume, Hydrological Science Journal, Vol 42, No 1 pp 15-33
Wennell W.G., 1965, Water Resource of Rhodesia, in Collins M.O. Rhodesia, 1965, Its
Natural Resources and Economic Development, Collins
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Droughts, Hydrology Paper No. 23., Colorado University, Fort Collins, Colorado, USA
13
Tables
Table 1
Summary of area affected considering an index on MAR
SEASO
PERCENTAGE OF AREA OF MZINGWANE AFFECTED
N
0>=Index<0.
0.25<=Index<0.
0.5
0.75>=Index
Index>=
25
5
>=Index<0.75
<1
1
1984/85
3%
6%
27%
21%
43%
1985/86
4%
48%
34%
13%
1%
1986/87
14%
79%
7%
0%
0%
1987/88
3%
5%
1%
2%
88%
1988/89
11%
26%
60%
3%
0%
1989/90
12%
23%
42%
22%
1%
1990/91
15%
22%
35%
23%
5%
1991/92
39%
58%
3%
0%
0%
1992/93
13%
26%
35%
16%
10%
1993/94
13%
12%
51%
23%
1%
14
Figures and figure captions
Fig 1. Provinces forming the Mzingwane primary catchment
15
Fig 2. Illustration of fixed threshold of flow
16
Fig 3. Drought runoff for cumulative catchment outlet of NC
17
Fig 4. Mzingwane1:50, 1year drought and 1:10, 1year drought
18
Fig 5. Index on MAR for 1984/85 and 1985/86
19
Fig 6. Index on MAR for 1986/87 and 1987/88
20
Fig 7. Index on MAR for 1988/89 and 1989/90
21
Fig 8. Index on MAR for 1990/91and 1991/92
22
Fig 9. Index on MAR for 1992/93 and 1993/94
23
Fig 10. Index on 50% and 80% exceedences for 1991/92
24
Fig 11. Index on 95% and 98% exceedences for 1991/92
25
Fig 12. Indices on 1:10, 4year and 1:15, 4 year drought for 1991/92
26
Fig 13. Population for 1992 and 1991/92 runoff indexed on 1:10 year, 4 years drought flow
27